摘要
研究一类具HollingⅡ功能性函数的含扩散与时滞Prey-Predator系统,利用上下解及比较原理,通过周期抛物系统ui(t,x)/t-Aiui(t,x)=ui(t,x)[ai(t,x)-bi(t,x)ui(tx,x)](i=1,2)的周期解得到系统的上下解,证明了系统在对应的特征方程的主特征值σ1(a1)≥0,σ1(a2)>0时存在全局渐近稳定的平凡解(0,0),当σ1(a1)≥0,σ1(a2)<0时系统存在全局渐近稳定的半平凡解(0,Θ2(t,x)),当σ1(a1)<0,σ1(a2+1)≥0时系统存在全局渐近稳定的半平凡解(θ1(t,x),0),并获得当σ1(a1)<0,σ1(a2)<0时系统存在一对T-周期拟解的充分条件,且对任意的非负初值函数这对周期拟解构成此系统的一个吸引子。
The existence and stability of periodic solution in Prey-Predator system with diffusion,time-delay and Holling type II are investigated by using the method of upper and lower solutions and comparison principle.It is shown that the globally asymptotically stale trivial solution(0,0) when σ1(a1)≥0,σ1(a2)0,the globally asymptotically stale semi-trivial periodic solutions(0,Θ2(t,x)),(θ1(t,x),0) when σ1(a1)≥0,σ1(a2)0 and σ1(a1)0,σ1(a2+1)≥0 of the system by construction of a pair of upper and lower solution of parabolic periodic systemui(t,x)/t-Aiui(t,x)=ui(t,x)[ai(t,x)-bi(t,x)ui(tx,x)](i=1,2).It was obtained that the system have a pair of T-periodic quasi-solutions and the sector between the quasi-solutions is an attractor of the system with respect to every nonnegative initial function.
出处
《重庆师范大学学报(自然科学版)》
CAS
2010年第6期43-47,共5页
Journal of Chongqing Normal University:Natural Science
基金
四川民族学院资助项目(No.2009[8])